0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.14/0.35 % Computer : n012.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Jul 13 11:26:46 EDT 2021 0.14/0.35 % CPUTime : 0.20/0.47 %----THF division 0.20/0.48 ------- cvc5-thf casc 28 : /export/starexec/sandbox/benchmark/theBenchmark.p at 120... 0.20/0.48 --- Run --ho-elim --full-saturate-quant at 10... 10.60/10.84 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 10.67/10.87 % SZS status Theorem for theBenchmark 10.67/10.88 % SZS output start Proof for theBenchmark 10.67/10.88 (proof 10.67/10.88 (let ((_let_1 (not (forall ((X1 $$unsorted)) (= ((addition X1) X1) X1))))) (let ((_let_2 (sup emptyset))) (let ((_let_3 (= _let_2 zero))) (let ((_let_4 (forall ((X $$unsorted)) (= (sup (singleton X)) X)))) (let ((_let_5 (= crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (X X1) (Y Y1) (= A ((multiplication X1) Y1)))))))) (let ((_let_6 (= addition (lambda ((X $$unsorted) (Y $$unsorted)) (sup ((union (singleton X)) (singleton Y))))))) (let ((_let_7 (= unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (F Y) (Y X))))))) (let ((_let_8 (= supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (F Y) (= (sup Y) X))))))) (let ((_let_9 (= singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_10 (= union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (X U) (Y U)))))) (let ((_let_11 (= emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_12 (ho_8 k_7 skv_26))) (let ((_let_13 (= skv_26 (ho_13 k_12 _let_12)))) (let ((_let_14 (ho_8 k_24 skv_26))) (let ((_let_15 (= skv_26 (ho_13 k_12 _let_14)))) (let ((_let_16 (= _let_12 _let_14))) (let ((_let_17 (forall ((X1 $$unsorted)) (= X1 (ho_13 k_12 (ho_8 k_7 X1)))))) (let ((_let_18 (not _let_13))) (let ((_let_19 (not _let_17))) (let ((_let_20 (not (forall ((X1 $$unsorted)) (= X1 (sup (ll_6 X1))))))) (let ((_let_21 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))))) (let ((_let_22 (ASSUME |:args| (_let_10)))) (let ((_let_23 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (MACRO_SR_EQ_INTRO |:args| (_let_9 7 12))))) (let ((_let_24 (EQ_RESOLVE (ASSUME |:args| (_let_8)) (MACRO_SR_EQ_INTRO |:args| (_let_8 7 12))))) (let ((_let_25 (EQ_RESOLVE (ASSUME |:args| (_let_7)) (MACRO_SR_EQ_INTRO |:args| (_let_7 7 12))))) (let ((_let_26 (EQ_RESOLVE (ASSUME |:args| (_let_6)) (MACRO_SR_EQ_INTRO _let_25 _let_24 _let_23 _let_22 _let_21 |:args| (_let_6 7 12))))) (let ((_let_27 (EQ_RESOLVE (ASSUME |:args| (_let_5)) (MACRO_SR_EQ_INTRO |:args| (_let_5 7 12))))) (let ((_let_28 (EQ_RESOLVE (SYMM (ASSUME |:args| (_let_3))) (MACRO_SR_EQ_INTRO _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 |:args| ((= zero _let_2) 7 12))))) (let ((_let_29 (EQ_RESOLVE (ASSUME |:args| (_let_1)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_1 7 12)) (MACRO_SR_EQ_INTRO _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 |:args| ((not (forall ((X1 $$unsorted)) (= X1 ((addition X1) X1)))) 7 12)) (PREPROCESS |:args| ((= (not (forall ((X1 $$unsorted)) (= X1 (sup (lambda ((BOUND_VARIABLE_702 $$unsorted)) (= X1 BOUND_VARIABLE_702)))))) _let_20))) (PREPROCESS |:args| ((= _let_20 _let_19))))))) (let ((_let_30 (20))) (let ((_let_31 (forall ((X $$unsorted)) (= X (ho_13 k_12 (ho_8 k_24 X)))))) (let ((_let_32 (forall ((X $$unsorted)) (= X (sup (ll_1 X)))))) (let ((_let_33 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_4 7 12)) (MACRO_SR_EQ_INTRO _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 |:args| ((forall ((X $$unsorted)) (= X (sup (singleton X)))) 7 12)) (PREPROCESS |:args| ((= (forall ((X $$unsorted)) (= X (sup (lambda ((BOUND_VARIABLE_562 $$unsorted)) (= X BOUND_VARIABLE_562))))) _let_32))) (PREPROCESS |:args| ((= _let_32 _let_31))))))) (let ((_let_34 (forall ((z $$unsorted)) (= (ho_9 (ho_8 k_7 skv_26) z) (ho_9 (ho_8 k_24 skv_26) z))))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_16))) (let ((_let_37 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_39 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_41 (forall ((u |u_(-> $$unsorted $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_11 v ii) (ite (= i ii) e (ho_11 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> $$unsorted $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_11 x z) (ho_11 y z)))) (= x y))))) (let ((_let_43 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (e $$unsorted) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_13 v ii) (ite (= i ii) e (ho_13 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_13 x z) (ho_13 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (e Bool) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_14 v ii) (ite (= i ii) e (ho_14 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_14 x z) (ho_14 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_16 v ii) (ite (= i ii) e (ho_16 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> $$unsorted $$unsorted $$unsorted)|) (e |u_(-> $$unsorted $$unsorted)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_19 v ii) (ite (= i ii) e (ho_19 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> $$unsorted $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> $$unsorted $$unsorted)|) (e $$unsorted) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_20 v ii) (ite (= i ii) e (ho_20 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_20 x z) (ho_20 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_22 v ii) (ite (= i ii) e (ho_22 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_22 x z) (ho_22 y z)))) (= x y))))) (let ((_let_57 (forall ((BOUND_VARIABLE_872 $$unsorted) (BOUND_VARIABLE_873 $$unsorted)) (= (ho_9 (ho_8 k_7 BOUND_VARIABLE_872) BOUND_VARIABLE_873) (= BOUND_VARIABLE_872 BOUND_VARIABLE_873))))) (let ((_let_58 (forall ((BOUND_VARIABLE_862 $$unsorted) (BOUND_VARIABLE_863 $$unsorted) (BOUND_VARIABLE_864 $$unsorted)) (= (ho_9 (ho_8 (ho_11 k_10 BOUND_VARIABLE_862) BOUND_VARIABLE_863) BOUND_VARIABLE_864) (or (= BOUND_VARIABLE_862 BOUND_VARIABLE_864) (= BOUND_VARIABLE_863 BOUND_VARIABLE_864)))))) (let ((_let_59 (forall ((BOUND_VARIABLE_937 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (BOUND_VARIABLE_850 $$unsorted)) (= (ho_9 (ho_16 k_15 BOUND_VARIABLE_937) BOUND_VARIABLE_850) (not (forall ((BOUND_VARIABLE_924 |u_(-> $$unsorted Bool)|)) (or (not (ho_14 BOUND_VARIABLE_937 BOUND_VARIABLE_924)) (not (= BOUND_VARIABLE_850 (ho_13 k_12 BOUND_VARIABLE_924)))))))))) (let ((_let_60 (forall ((BOUND_VARIABLE_962 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (BOUND_VARIABLE_837 $$unsorted)) (= (ho_9 (ho_16 k_17 BOUND_VARIABLE_962) BOUND_VARIABLE_837) (not (forall ((BOUND_VARIABLE_959 |u_(-> $$unsorted Bool)|)) (or (not (ho_14 BOUND_VARIABLE_962 BOUND_VARIABLE_959)) (not (ho_9 BOUND_VARIABLE_959 BOUND_VARIABLE_837))))))))) (let ((_let_61 (forall ((BOUND_VARIABLE_993 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_990 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_822 $$unsorted)) (= (ho_9 (ho_23 (ho_22 k_21 BOUND_VARIABLE_993) BOUND_VARIABLE_990) BOUND_VARIABLE_822) (not (forall ((BOUND_VARIABLE_598 $$unsorted) (BOUND_VARIABLE_599 $$unsorted)) (or (not (ho_9 BOUND_VARIABLE_993 BOUND_VARIABLE_598)) (not (ho_9 BOUND_VARIABLE_990 BOUND_VARIABLE_599)) (not (= BOUND_VARIABLE_822 (ho_20 (ho_19 k_18 BOUND_VARIABLE_598) BOUND_VARIABLE_599)))))))))) (let ((_let_62 (forall ((BOUND_VARIABLE_813 $$unsorted) (BOUND_VARIABLE_814 $$unsorted)) (= (ho_9 (ho_8 k_24 BOUND_VARIABLE_813) BOUND_VARIABLE_814) (= BOUND_VARIABLE_813 BOUND_VARIABLE_814))))) (let ((_let_63 (and (forall ((BOUND_VARIABLE_813 $$unsorted) (BOUND_VARIABLE_814 $$unsorted)) (= (ll_1 BOUND_VARIABLE_813 BOUND_VARIABLE_814) (= BOUND_VARIABLE_813 BOUND_VARIABLE_814))) (forall ((BOUND_VARIABLE_820 (-> $$unsorted Bool)) (BOUND_VARIABLE_821 (-> $$unsorted Bool)) (BOUND_VARIABLE_822 $$unsorted)) (= (ll_2 BOUND_VARIABLE_820 BOUND_VARIABLE_821 BOUND_VARIABLE_822) (not (forall ((BOUND_VARIABLE_598 $$unsorted) (BOUND_VARIABLE_599 $$unsorted)) (or (not (BOUND_VARIABLE_820 BOUND_VARIABLE_598)) (not (BOUND_VARIABLE_821 BOUND_VARIABLE_599)) (not (= ((multiplication BOUND_VARIABLE_598) BOUND_VARIABLE_599) BOUND_VARIABLE_822))))))) (forall ((BOUND_VARIABLE_836 (-> (-> $$unsorted Bool) Bool)) (BOUND_VARIABLE_837 $$unsorted)) (= (ll_3 BOUND_VARIABLE_836 BOUND_VARIABLE_837) (not (forall ((BOUND_VARIABLE_644 (-> $$unsorted Bool))) (or (not (BOUND_VARIABLE_836 BOUND_VARIABLE_644)) (not (BOUND_VARIABLE_644 BOUND_VARIABLE_837))))))) (forall ((BOUND_VARIABLE_849 (-> (-> $$unsorted Bool) Bool)) (BOUND_VARIABLE_850 $$unsorted)) (= (ll_4 BOUND_VARIABLE_849 BOUND_VARIABLE_850) (not (forall ((BOUND_VARIABLE_629 (-> $$unsorted Bool))) (or (not (BOUND_VARIABLE_849 BOUND_VARIABLE_629)) (not (= (sup BOUND_VARIABLE_629) BOUND_VARIABLE_850))))))) (forall ((BOUND_VARIABLE_862 $$unsorted) (BOUND_VARIABLE_863 $$unsorted) (BOUND_VARIABLE_864 $$unsorted)) (= (ll_5 BOUND_VARIABLE_862 BOUND_VARIABLE_863 BOUND_VARIABLE_864) (or (= BOUND_VARIABLE_862 BOUND_VARIABLE_864) (= BOUND_VARIABLE_863 BOUND_VARIABLE_864)))) (forall ((BOUND_VARIABLE_872 $$unsorted) (BOUND_VARIABLE_873 $$unsorted)) (= (ll_6 BOUND_VARIABLE_872 BOUND_VARIABLE_873) (= BOUND_VARIABLE_872 BOUND_VARIABLE_873)))))) (let ((_let_64 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (PREPROCESS_LEMMA |:args| (_let_63)) (PREPROCESS |:args| ((= _let_63 (and _let_62 _let_61 _let_60 _let_59 _let_58 _let_57))))) (PREPROCESS |:args| ((and _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_37 _let_38)))) |:args| ((and _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_37 _let_38))))) (let ((_let_65 (_let_37))) (let ((_let_66 (ho_9 _let_14 skv_67))) (let ((_let_67 (ho_9 _let_12 skv_67))) (let ((_let_68 (= _let_67 _let_66))) (let ((_let_69 (= skv_26 skv_67))) (let ((_let_70 (= _let_67 _let_69))) (let ((_let_71 (= _let_66 _let_69))) (let ((_let_72 (ho_9 _let_14 skv_26))) (let ((_let_73 (not _let_67))) (let ((_let_74 (_let_68))) (let ((_let_75 (_let_57))) (let ((_let_76 (skv_26 skv_67))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_75) |:args| _let_76) |:args| _let_75)) (AND_ELIM _let_64 |:args| (5)) |:args| (_let_70 false _let_57)))) (let ((_let_78 (not _let_70))) (let ((_let_79 (_let_70))) (let ((_let_80 (AND_ELIM _let_64 |:args| (0)))) (let ((_let_81 (_let_62))) (let ((_let_82 (ASSUME |:args| _let_81))) (let ((_let_83 (not _let_69))) (let ((_let_84 (not _let_72))) (let ((_let_85 (not _let_66))) (let ((_let_86 (_let_35))) (let ((_let_87 (and _let_16 _let_15))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG |:args| (_let_87)) (IMPLIES_ELIM (SCOPE (TRANS (SYMM (SYMM (ASSUME |:args| (_let_15)))) (CONG (REFL |:args| (k_12)) (SYMM (ASSUME |:args| (_let_16))) |:args| (23 ho_13))) |:args| (_let_16 _let_15))) |:args| (true _let_87)) |:args| ((or _let_13 (not _let_15) (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_36)) |:args| ((or _let_35 _let_16 (not _let_36)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_86)) |:args| _let_86)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_35) _let_34))) (REFL |:args| ((not _let_68))) |:args| _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 |:args| (_let_71)) |:args| ((or _let_85 _let_69 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 |:args| _let_76) |:args| _let_81)) _let_80 |:args| (_let_71 false _let_62)) (REORDERING (CNF_EQUIV_POS2 |:args| _let_79) |:args| ((or _let_67 _let_83 _let_78))) _let_77 (REORDERING (CNF_EQUIV_NEG1 |:args| _let_74) |:args| ((or _let_67 _let_66 _let_68))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME |:args| (_let_85)))) (CONG (REFL |:args| (_let_14)) (SYMM (ASSUME |:args| (_let_69))) |:args| (23 ho_9)) (TRUE_INTRO (ASSUME |:args| (_let_72))))) |:args| (_let_72 _let_69 _let_85))) (CONG (REFL |:args| (_let_84)) (REFL |:args| (_let_83)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_85) _let_66))) |:args| _let_30)) |:args| ((or _let_84 _let_66 _let_83))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_82 |:args| (skv_26 skv_26)) |:args| _let_81))) _let_80 |:args| (_let_72 false _let_62)) (REORDERING (CNF_EQUIV_POS1 |:args| _let_79) |:args| ((or _let_73 _let_69 _let_78))) _let_77 (CNF_EQUIV_NEG2 |:args| _let_74) |:args| ((or _let_68 _let_73) false _let_72 false _let_69 false _let_70 true _let_66)) |:args| (_let_68 false _let_71 true _let_69 false _let_70 false _let_66 true _let_67)) |:args| (_let_34 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_65) |:args| (_let_12 _let_14)) |:args| _let_65)) (AND_ELIM _let_64 |:args| (24)) |:args| (_let_36 false _let_37)) |:args| (_let_16 false _let_34 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 |:args| (skv_26)) |:args| (_let_31))) _let_33 |:args| (_let_15 false _let_31)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_29) |:args| (_let_19))) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_19) _let_17))) (REFL |:args| (_let_18)) |:args| _let_30)) _let_29 |:args| (_let_18 true _let_17)) |:args| (false false _let_16 false _let_15 true _let_13)) |:args| (_let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 (forall ((X $$unsorted)) (= ((multiplication X) one) X)) (forall ((X $$unsorted)) (= ((multiplication one) X) X)) _let_4 (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= ((multiplication (sup X)) (sup Y)) (sup ((crossmult X) Y)))) _let_3 (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (sup (supset X)) (sup (unionset X)))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (= ((leq X1) X2) (= ((addition X1) X2) X2))) _let_1 (not false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 10.67/10.88 ) 10.67/10.88 % SZS output end Proof for theBenchmark 10.67/10.88 EOF